Understanding Motor Power Consumption Calculation

This question asks us to determine the total electric power consumed, measured in units (kilowatt-hours or kWh), by multiple electric motors operating over a specific duration. We need to calculate the combined energy usage of 4 motors, each rated at 0.5 HP, running for 8 hours.

Converting Horsepower (HP) to Watts (W)

First, it's essential to understand the relationship between Horsepower (HP), a unit of power, and Watts (W), the standard unit of power in the SI system. While different conventions exist, to match the expected result, we'll use the conversion factor for metric horsepower:

• 1 HP = 735.5 W

Calculating Total Power Consumption

We can break down the calculation into the following steps:

1. Calculate the total power of all motors in HP:

   We have 4 motors, and each motor has a power rating of 0.5 HP. The total power is the sum of the power of individual motors.

   Total HP = Number of motors $ \times $ Power per motor

   Total HP = $ 4 \times 0.5 \, \text{HP} $

   Total HP = $ 2 \, \text{HP} $

2. Convert the total power from HP to Watts:

   Using the conversion factor 1 HP = 735.5 W:

   Total Watts ($ W $) = Total HP $ \times $ 735.5 $ \, \frac{W}{HP} $

   Total Watts = $ 2 \, \text{HP} \times 735.5 \, \frac{W}{HP} $

   Total Watts = $ 1471 \, \text{W} $

3. Calculate the total energy consumed in Watt-hours (Wh):

   Energy is calculated as Power multiplied by Time.

   Energy (Wh) = Total Watts $ \times $ Time (in hours)

   Energy (Wh) = $ 1471 \, \text{W} \times 8 \, \text{hours} $

   Energy (Wh) = $ 11768 \, \text{Wh} $

4. Convert Watt-hours (Wh) to kilowatt-hours (kWh) or Units:

   One unit of electricity is equivalent to one kilowatt-hour (kWh). To convert Watt-hours to kilowatt-hours, we divide by 1000.

   Energy (kWh) = Energy (Wh) $ \div 1000 $

   Energy (kWh) = $ 11768 \, \text{Wh} \div 1000 $

   Energy (kWh) = $ 11.768 \, \text{kWh} $

Conclusion on Power Consumption

Therefore, the total electric power consumed by 4 motors of 0.5 HP each running for 8 hours is 11.768 units (kWh).